The superfluid drag-coefficient of a weakly interacting three-component Bose-Einstein condensate is computed on a square optical lattice deep in the superfluid phase, starting from a Bose-Hubbard model with component-conserving, on-site interactions and nearest-neighbor hopping. At the meanfield level, Rayleigh-Schrödinger perturbation theory is employed to provide an analytic expression for the drag density. In addition, the Hamiltonian is diagonalized numerically to compute the drag within mean-field theory at both zero and finite temperatures to all orders in inter-component interactions. Moreover, path integral Monte Carlo simulations, providing results beyond mean-field theory, have been performed to support the mean-field results. In the two-component case the drag increases monotonically with the magnitude of the inter-component interaction γAB between the two components A and B. The increase is independent of the sign of the inter-component interaction. This no longer holds when an additional third component C is included. Instead of increasing monotonically, the drag can either be strengthened or weakened depending on the details of the interaction strengths, for weak and moderately strong interactions. The general picture is that the drag-coefficient between component A and B is a non-monotonic function of the intercomponent interaction strength γAC between A and a third component C. For weak γAC compared to the direct interaction γAB between A and B, the drag-coefficient between A and B can decrease, contrary to what one naively would expect. When γAC is strong compared to γAB, the drag between A and B increases with increasing γAC , as one would naively expect. We attribute the subtle reduction of ρ d,AB with increasing γAC , which has no counterpart in the two-component case, to a renormalization of the inter-component scattering vertex γAB via intermediate excited states of the third condensate C. We briefly comment on how this generalizes to systems with more than three components.

Constraints on the cosmic history of self-interacting Bose-Einstein condensed (SIBEC) dark matter (DM) are obtained using the cosmic microwave background (CMB), baryonic acoustic oscillations (BAO), growth factor measurements, and type Ia supernovae (SNIa) distances. Four scenarios are considered, one with purely SIBEC-DM, and three in which SIBEC-DM is the final product of some transition from different initial states, which are either cold, warm, or has a constant equation of state. Using a fluid approximation for the self-interacting scalar field it is found that in the simplest scenario of purely SIBEC-DM the self-interaction necessary for solving the cusp-core problem, with core-radii of low-mass halos of order R c ≳ 1kpc, is excluded at 2.4σ, or 98.5% confidence. Introducing a transition, however, relaxes this constraint, but the transitions are preferred to be after matter-radiation equality, and the initial phase to be cold.

Aims. The aim of the present work is to better understand the gravitational drag forces, also referred to as dynamical friction, acting on massive objects moving through a self-interacting Bose-Einstein condensate, also known as a superfluid, at finite temperatures. This is relevant for models of dark matter consisting of light scalar particles with weak self-interactions that require nonzero temperatures, or that have been heated inside galaxies. Methods. We derived expressions for dynamical friction using linear perturbation theory, and compared these to numerical simulations in which nonlinear effects are included. After testing the linear result, it was applied to the Fornax dwarf spheroidal galaxy, and two of its gravitationally bound globular clusters. Dwarf spheroidals are well-suited for indirectly probing properties of dark matter, and so by estimating the rate at which these globular clusters are expected to sink into their host halo due to dynamical friction, we inferred limits on the superfluid dark matter parameter space. Results. The dynamical friction in a finite-temperature superfluid is found to behave very similarly to the zero-temperature limit, even when the thermal contributions are large. However, when a critical velocity for the superfluid flow is included, the friction force can transition from the zero-temperature value to the value in a conventional thermal fluid. Increasing the mass of the perturbing object induces a similar transition to when lowering the critical velocity. When applied to two of Fornax’s globular clusters, we find that the parameter space preferred in the literature for a zero-temperature superfluid yields decay times that are in agreement with observations. However, the present work suggests that increasing the temperature, which is expected to change the preferred parameter space, may lead to very small decay times, and therefore pose a problem for finite-temperature superfluid models of dark matter.

Aims. We intend to understand cosmological structure formation within the framework of superfluid models of dark matter with finite temperatures. Of particular interest is the evolution of small-scale structures where the pressure and superfluid properties of the dark matter fluid are prominent. We compare the growth of structures in these models with the standard cold dark matter paradigm and non-superfluid dark matter. Methods. The equations for superfluid hydrodynamics were computed numerically in an expanding ΛCDM background with spherical symmetry; the effect of various superfluid fractions, temperatures, interactions, and masses on the collapse of structures was taken into consideration. We derived the linear perturbation of the superfluid equations, giving further insights into the dynamics of the superfluid collapse. Results. We found that while a conventional dark matter fluid with self-interactions and finite temperatures experiences a suppression in the growth of structures on smaller scales, as expected due to the presence of pressure terms, a superfluid can collapse much more efficiently than was naively expected due to its ability to suppress the growth of entropy perturbations and thus gradients in the thermal pressure. We also found that the cores of the dark matter halos initially become more superfluid during the collapse, but eventually reach a point where the superfluid fraction falls sharply. The formation of superfluid dark matter halos surrounded by a normal fluid dark matter background is therefore disfavored by the present work.

Fully 3D cosmological simulations of scalar field dark matter with self-interactions, also known as Bose-Einstein condensate dark matter, are performed using a set of effective hydrodynamic equations. These are derived from the non-linear Schrödinger equation by performing a smoothing operation over scales larger than the de Broglie wavelength, but smaller than the self-interaction Jeans' length. The dynamics on the de Broglie scale become an effective thermal energy in the hydrodynamic approximation, which is assumed to be subdominant in the initial conditions, but become important as structures collapse and the fluid is shock-heated. The halos that form have Navarro-Frenk-White envelopes, while the centers are cored due to the fluid pressures (thermal + self-interaction), confirming the features found by Dawoodbhoy et al. ( 2021) using 1D simulations under the assumption of spherical symmetry. The core radii are largely determined by the self-interaction Jeans' length, even though the effective thermal energy eventually dominates over the self-interaction energy everywhere, a result that is insensitive to the initial ratio of thermal energy to interaction energy, provided it is sufficiently small to not affect the linear and weakly non-linear regimes. Scaling relations for the simulated population of halos are compared to Milky Way dwarf spheroidals and nearby galaxies, assuming a Burkert halo profile, and are found to not match, although they conform better with observations compared to fuzzy dark matter-only simulations.